Electrophoresis is the motion of charged dispersed particles relative to a fluid in a uniform electric field, and is typically used to separate macromolecules (e.g. DNA and proteins), to assemble colloidal structures, and to transport particles in nano-fluidic and micro-fluidic devices and displays. For example, electrophoresis is utilized to transport particles in micro-fluidic displays, such as that used by the KINDLE™ electronic reader, and other electrophoretic or e-ink displays. Typically, the fluid, such as water, utilized as the electrophoretic medium is isotropic, whereby the electrophoretic velocity of a dispersed particle in the fluid is directly proportional to the applied electric field. Because of this linear dependence, only a direct current (DC) electric field can be used to drive the particles through the fluid. However, the use of an alternating current (AC) electric field to drive the particles through the fluid is more desirable, as it prevents electrolysis, i.e., electrochemical reactions near the electrodes resulting in degradation of the medium. Furthermore, the use of AC electric fields to drive the particles allows one to create steady flows of particles, as the AC field avoids accumulation of the electric charges near the electrodes screening the electric field. Furthermore, the direction of electrophoretic motion of the particles in an isotropic fluid, such as water, is typically parallel or antiparallel to the applied electric field, which makes it difficult to design three-dimensional trajectories of the particles. To move the particle in a direction that is not collinear with the direction of electric field, one needs to design the shape or to modify the surface properties of particles.
Therefore, there is a need for a method of moving particles by electric field in which the driving force can be an AC field and in which the trajectory of the particle can follow a predetermined 3D pathway. In addition, there is a need for a method of moving particles, such as liquid droplets or gas bubbles, by electrophoresis in a liquid crystal using direct current (DC) or alternating current (AC) electric fields. Moreover, there is a need for a method of moving particles, such as liquid droplets and gas bubbles, through a nematic liquid crystal (LC), whereby the electrophoretic velocity is proportional to the square of the applied voltage, allowing the particles to be moved by an AC electric field. In addition, there is a need for a method of moving particles, such as liquid droplets and gas bubbles, by electrophoresis through a liquid crystal upon application of an AC electric field, such that the liquid crystal orientation around the particle is distorted, so as to break the fore-aft or right-left symmetry of the liquid crystal surrounding the particle. Furthermore, there is a need for a method of moving particles, such as liquid droplets and gas bubbles, by electrophoresis through a liquid crystal, such that the direction of electrophoretic motion of the particle is controlled by three factors: the direction of the electric field, the shape of the particle in conjunction with the local orientation of the liquid crystal around the particle, and an orientationally ordered nematic liquid crystal far from the particle, so as to allow three-dimensional control of trajectories of moving particles to be constructed.